Series-form solutions of generalized fractional-fisher models with uncertainties using hybrid approach in Caputo sense

Abstract

The field of fuzzy calculus has emerged as a powerful mathematical tool which can effectively deal with uncertainties and impressions that are common in real-world situations. In particular, it has proven useful in modeling and analysis of complex biological systems with uncertain parameters. The current study focuses on analysis of (n+1)-dimensional fractional Fisher equations (FFEs) in fuzzy environment. The objective is to provide semi-analytical solutions for fuzzy (n+1)- dimensional FFEs by considering Caputo-gH fractional derivative. The uncertainty in initial conditions is injected through triangular fuzzy numbers and obtained fuzzy (n+1)-dimensional FFEs are solved using hybrid of homotopy perturbation with Laplace transform in fuzzy-Caputo sense, which provides a powerful mathematical framework for examining complex behavior. The derived series solutions are validated against existing results from the literature and found to be improved. The obtained results are analyzed by means of determining the fuzzy solutions and residual errors at varying fractional orders, membership function, spatial coordinate x, and time t. These analytical findings are visualized in graphical form for ease of comprehension. The conducted study yields significant insights about the behavior of fractional model having uncertain conditions, and highlights the efficiency of proposed methodology. The results of this study have important implications for understanding the dynamics of biological systems with uncertainty, and hence can be useful in wide variety of applications in different fields such as ecology, epidemiology, and economics.